PMC National MDCAT Logical Reasoning Logical Deductions — Set 2

PMC National MDCAT Logical Reasoning Logical Deductions — Set 2

1. Question 1

   Q1. If all X are Y and no Y is Z, which conclusion is valid?

   • A) All X are Z
   • B) No X is Z
   • C) Some X are Z
   • D) Some X are not Y

   Answer: No X is Z

   Explanation: B follows by syllogism. A contradicts premises via transitivity. USAT, HAT and MDCAT analytical sections repeat this pattern.

2. Question 2

   Q2. A statement says 'If P then Q'. If Q is false, what can be concluded?

   • A) P is false
   • B) Q is true
   • C) P is true
   • D) Q is false

   Answer: P is false

   Explanation: A is contrapositive. B assumes inverse fallacy which is invalid. USAT, HAT and MDCAT analytical sections repeat this pattern.

3. Question 3

   Q3. Given 'All doctors are professionals' and 'Some professionals are athletes', which conclusion is guaranteed?

   • A) All doctors are athletes
   • B) Some doctors are athletes
   • C) No athlete is a doctor
   • D) Some professionals are doctors

   Answer: Some professionals are doctors

   Explanation: D follows by converse. A assumes false transitivity between premises. USAT, HAT and MDCAT analytical sections repeat this pattern.

4. Question 4

   Q4. If 'No reptiles are mammals' and 'All lizards are reptiles', which conclusion is logically valid?

   • A) Some lizards are mammals
   • B) No lizard is a mammal
   • C) All mammals are lizards
   • D) Some reptiles are mammals

   Answer: No lizard is a mammal

   Explanation: B follows by syllogism. A contradicts premises via transitivity. USAT, HAT and MDCAT analytical sections repeat this pattern.

5. Question 5

   Q5. Which of these is the inverse of 'If it snows, schools close'? A) If schools close, it snows B) If it doesn't snow, schools don't close C) If schools don't close, it didn't snow D) If it snows, schools don't close

   • A) A
   • B) B
   • C) C
   • D) D

   Answer: B

   Explanation: B is inverse. A is converse fallacy which is logically invalid. USAT, HAT and MDCAT analytical sections repeat this pattern.

6. Question 6

   Q6. Given 'All A are B' and 'Some B are C', which conclusion is necessarily true?

   • A) Some A are C
   • B) No A is C
   • C) Some C are A
   • D) Some B are A

   Answer: Some B are A

   Explanation: D follows by converse. A assumes false transitivity between premises. USAT, HAT and MDCAT analytical sections repeat this pattern.

7. Question 7

   Q7. A study claims 'All patients with X have Y symptoms'. A doctor observes Y symptoms in a patient. What can be concluded?

   • A) The patient has X
   • B) The patient lacks X
   • C) Y symptoms imply X
   • D) Y symptoms may occur without X

   Answer: Y symptoms may occur without X

   Explanation: D acknowledges converse fallacy. A assumes false equivalence. USAT, HAT and MDCAT analytical sections repeat this pattern.

8. Question 8

   Q8. Which of these statements is logically equivalent to 'If P then Q'? A) If not P then not Q B) If not Q then not P C) If Q then P D) P if and only if Q

   • A) A
   • B) B
   • C) C
   • D) D

   Answer: B

   Explanation: B is contrapositive. A is inverse fallacy which differs in truth value.

9. Question 9

   Q9. Given 'Some novels are biographies' and 'All biographies are non-fiction', which conclusion is valid?

   • A) Some novels are non-fiction
   • B) All novels are non-fiction
   • C) No novel is biography
   • D) Some non-fiction are not novels

   Answer: Some novels are non-fiction

   Explanation: A follows via transitivity. B assumes false universal conclusion. USAT, HAT and MDCAT analytical sections repeat this pattern.

10. Question 10

    Q10. Which statement invalidates the argument: 'If it rains, the ground gets wet. The ground is wet, therefore it rained.'?

    • A) The ground can be wet without rain
    • B) Rain always produces wet ground
    • C) Wet ground implies rain
    • D) Rain is necessary for wet ground

    Answer: The ground can be wet without rain

    Explanation: A shows converse fallacy. C repeats the invalid assumption. USAT, HAT and MDCAT analytical sections repeat this pattern.

11. Question 11

    Q11. Given 'No squares are circles' and 'All circles are shapes', which conclusion is valid?

    • A) Some squares are not shapes
    • B) All squares are shapes
    • C) No shapes are squares
    • D) Some shapes are not squares

    Answer: Some shapes are not squares

    Explanation: D follows via universal premise. A assumes false particular conclusion. USAT, HAT and MDCAT analytical sections repeat this pattern.

12. Question 12

    Q12. If 'All metals conduct electricity' and 'Copper is a metal', which conclusion is valid?

    • A) Copper conducts electricity
    • B) Copper is non-metallic
    • C) All conductors are copper
    • D) No copper conducts electricity

    Answer: Copper conducts electricity

    Explanation: A follows syllogism. C assumes false converse relationship. USAT, HAT and MDCAT analytical sections repeat this pattern.

13. Question 13

    Q13. A logical system defines P → Q and Q → R. Which conclusion is valid?

    • A) P → R
    • B) R → P
    • C) P ↔ Q
    • D) Q ↔ R

    Answer: P → R

    Explanation: A follows hypothetical syllogism. B reverses logical sequence. USAT, HAT and MDCAT analytical sections repeat this pattern.

14. Question 14

    Q14. Given 'All cats are mammals' and 'Some mammals are dogs', which conclusion is valid?

    • A) Some cats are dogs
    • B) All mammals are cats
    • C) Some mammals are not cats
    • D) No dog is a cat

    Answer: Some mammals are not cats

    Explanation: C follows by converse. A assumes false transitivity between premises. USAT, HAT and MDCAT analytical sections repeat this pattern.

15. Question 15

    Q15. If 'If A then B' is true and B is true, what can be concluded?

    • A) A is true
    • B) A is false
    • C) B implies A
    • D) B does not imply A

    Answer: B does not imply A

    Explanation: D is valid since B's truth doesn't confirm A. A is converse fallacy.

16. Question 16

    Q16. Given 'No birds are reptiles' and 'All reptiles are cold-blooded', which conclusion is valid?

    • A) Some birds are cold-blooded
    • B) No bird is cold-blooded
    • C) All cold-blooded are birds
    • D) Some cold-blooded are not birds

    Answer: Some cold-blooded are not birds

    Explanation: D follows via universal premises. B assumes false particular conclusion. USAT, HAT and MDCAT analytical sections repeat this pattern.

17. Question 17

    Q17. A statement says 'All students passed the exam' is false. Which must be true?

    • A) No student passed
    • B) Some students failed
    • C) All students failed
    • D) Some students passed

    Answer: Some students failed

    Explanation: B is logical negation. A is extreme opposite of original statement. USAT, HAT and MDCAT analytical sections repeat this pattern.

18. Question 18

    Q18. If 'Some A are B' and 'Some B are C', which conclusion is necessarily true?

    • A) Some A are C
    • B) No A is C
    • C) Some C are A
    • D) Some A are not C

    Answer: Some A are not C

    Explanation: D isn't necessarily true. No valid conclusion follows from these premises. USAT, HAT and MDCAT analytical sections repeat this pattern.

19. Question 19

    Q19. Given 'If P then Q' is false, which statement must be true?

    • A) P is true and Q is true
    • B) P is true and Q is false
    • C) P is false and Q is true
    • D) P is false and Q is false

    Answer: P is true and Q is false

    Explanation: B is the only case where implication is false. A makes implication true.

20. Question 20

    Q20. Given 'All X are Y' and 'No Y is Z', which conclusion is valid?

    • A) All X are Z
    • B) No X is Z
    • C) Some X are Z
    • D) Some X are not Y

    Answer: No X is Z

    Explanation: B follows by syllogism. A contradicts premises via transitivity. USAT, HAT and MDCAT analytical sections repeat this pattern.